Scattering from multilayer thin films: theory and experiment

A theoretical method is described for calculating the angular scattering curve for any given thin-film multilayer in which the various surfaces and interfaces are assumed to be rough. The energy that is scattered in any particular direction depends on two factors. The first is solely a function of the characteristics of the ideal multilayer and the observation conditions. The second depends on the roughnesses of the various surfaces, that is, on their autocorrelation and cross-correlation functions. The expressions that are obtained are completely general because no restrictive hypothesis has been developed on the relationship that may exist between the roughnesses of the various interfaces. The principal features of the apparatus used for the scattering measurements are briefly described. Next, several results of calculation and measurement are given as illustrations. The measurements show that polished surfaces of high optical quality often show marked anisotropy.